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Combining Inequalities: Add em up!

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n2739178
 Post subject: Combining Inequalities: Add em up!
 Post Posted: Mon Jul 11, 2011 4:54 pm 
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Posts: 27
Hi all - in the MGMAT book for Equations, Inequalities and VICS, there is a bit about adding up inequalities... However, can someone explain why you can actually add up inequalities such as the ones in the question below? How do you know that in this case, you can't do this --> a + d < c + b?


here is the example:

Is a + 2b < c + 2d?

(1) a < c
(2) d > b


And the answer:


For this problem, we can add the inequalities together to make them match the question.
First, we need to line up the inequalities so that they are all facing the same direction:
a < c
b < d

Then we can take the sum of the two inequalities to prove the result. We will need to add
the second inequality TWICE:
a < c
+ b< d
a+ b < c+ d
+ b< d
a+2b < c+ 2d
If you use both statements, you can answer the question. Therefore the answer is (C).



thanks!
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jnelson0612
 Post subject: Re: Combining Inequalities: Add em up!
 Post Posted: Mon Jul 25, 2011 1:03 pm 
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ManhattanGMAT Staff


Posts: 1857
Hi there,
You are allowed to add inequality as long as the sign is pointing the same way for the inequalities you are adding together. Your example adds inequalities in which signs are facing opposite ways, and this is not allowed.

Sub in some numbers for a, b, c, and d, and see why this works (and doesn't work in the instance you suggested).

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Jamie Nelson
ManhattanGMAT Instructor
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